A company owns two dealerships, both of which sell cars and trucks. The first dealership sells a total of 225 cars and trucks. The second dealership sells twice as many cars and half as many trucks as the first dealership, and sells a total of 300 cars and trucks.
An equation for the total cars and trucks for dealership A:
An equation for the total cars and trucks for dealership B:
How many cars did dealership A sell?
How many trucks did the dealership B sell?
Let's represent the number of cars sold by the first dealership as "x" and the number of trucks as "y".
For dealership A:
x + y = 225
For dealership B:
2x + (1/2)y = 300
To find the number of cars dealership A sold, we substitute y = 225 - x in the equation for dealership B:
2x + (1/2)(225 - x) = 300
2x + 112.5 - 0.5x = 300
1.5x + 112.5 = 300
1.5x = 300 - 112.5
1.5x = 187.5
x = 187.5 / 1.5
x = 125
Thus, dealership A sold 125 cars.
To find the number of trucks dealership B sold, we substitute x = 125 in the equation for dealership A:
125 + y = 225
y = 225 - 125
y = 100
Thus, dealership B sold 100 trucks.
Let's solve this step by step:
Step 1: Assign variables
Let's assign variables to the unknowns:
Let x be the number of cars sold by Dealership A.
Let y be the number of trucks sold by Dealership A.
Step 2: Write equations for Dealership A
We know that Dealership A sells a total of 225 cars and trucks. So the equation for Dealership A is:
x + y = 225
Step 3: Write equations for Dealership B
We are given that Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A. Let's denote the number of cars sold by Dealership B as 2x (twice as many as Dealership A) and the number of trucks as (1/2)y (half as many as Dealership A). So the equation for Dealership B is:
2x + (1/2)y = 300
Step 4: Solve the equations
Now we can solve the equations simultaneously to find the values of x and y.
From equation 1, we have:
x + y = 225
From equation 2, we have:
2x + (1/2)y = 300
Multiply equation 2 by 2 to eliminate fractions:
4x + y = 600
Now we have a system of equations:
x + y = 225
4x + y = 600
Subtract equation 1 from equation 2 to eliminate y:
4x + y - (x + y) = 600 - 225
3x = 375
x = 375/3
x = 125
Substitute the value of x in equation 1 to find y:
125 + y = 225
y = 225 - 125
y = 100
Step 5: Answer the questions
From the calculations, we found:
Dealership A sold 125 cars.
Dealership B sold 100 trucks.
Therefore,
- The equation for the total cars and trucks for dealership A is: x + y = 225.
- The equation for the total cars and trucks for dealership B is: 2x + (1/2)y = 300.
- Dealership A sold 125 cars.
- Dealership B sold 100 trucks.
To solve this problem, let's assign variables to the unknown quantities. Let's say "x" represents the number of cars that dealership A sells, and "y" represents the number of trucks that dealership A sells.
The first dealership sells a total of 225 cars and trucks, so we can write the equation:
x + y = 225 (Equation 1)
Now let's calculate the number of cars and trucks sold at the second dealership. It sells twice as many cars as dealership A (2x) and half as many trucks (0.5y). The total number of cars and trucks sold at dealership B is 300, so we can write the equation:
2x + 0.5y = 300 (Equation 2)
Now we have two equations that can help us find the values of x and y.
To solve the system of equations, we can use substitution or elimination. In this case, let's use elimination.
Multiplying Equation 2 by 2 to get rid of decimals, we have:
4x + y = 600 (Equation 3)
Now, we can subtract Equation 1 from Equation 3 to eliminate the variable y:
4x + y - (x + y) = 600 - 225
3x = 375
x = 375/3
x = 125
So, dealership A sold 125 cars.
To find the number of trucks sold at dealership B, let's substitute the value of x into either Equation 1 or Equation 2:
From Equation 1:
125 + y = 225
y = 225 - 125
y = 100
Therefore, dealership B sold 100 trucks.
u mean 50
No, actually I made a mistake in my previous response. I apologize for the confusion.
Let's go through the solution again:
From Equation 1:
x + y = 225
From Equation 2:
2x + (1/2)y = 300
To eliminate the fractions, we can multiply Equation 2 by 2:
4x + y = 600
Now we can solve the system of equations:
x + y = 225 (Equation 1)
4x + y = 600 (Equation 2)
Subtract Equation 1 from Equation 2:
4x + y - (x + y) = 600 - 225
3x = 375
x = 375/3
x = 125
Substitute the value of x in Equation 1 to find y:
125 + y = 225
y = 225 - 125
y = 100
Therefore, dealership A sold 125 cars and dealership B sold 100 trucks. I apologize for the error in my previous response.
it say dealership B sold
33,50,98, or 49
Apologies for the confusion. Let's reevaluate the problem to find the correct answer.
We'll assign variables to the unknown quantities. Let's say "x" represents the number of cars that Dealership A sells, and "y" represents the number of trucks that Dealership A sells.
The first dealership sells a total of 225 cars and trucks, so we can write the equation:
x + y = 225 (Equation 1)
The second dealership sells twice as many cars as Dealership A and half as many trucks, so we have:
2x + (1/2)y = 300 (Equation 2)
Now we have the following system of equations to solve:
x + y = 225 (Equation 1)
2x + (1/2)y = 300 (Equation 2)
To eliminate the fraction in Equation 2, let's multiply both sides by 2:
4x + y = 600 (Equation 3)
Now we have the following system of equations to solve:
x + y = 225 (Equation 1)
4x + y = 600 (Equation 3)
Subtract Equation 1 from Equation 3 to find the value of x:
4x + y - (x + y) = 600 - 225
3x = 375
x = 375/3
x = 125
Now we can substitute the value of x in Equation 1 to find y:
125 + y = 225
y = 225 - 125
y = 100
Therefore, Dealership A sold 125 cars, and Dealership B sold 100 trucks. I apologize for the previous incorrect response.